Delta F=2 Observables and Fine-Tuning in a Warped Extra Dimension with Custodial Protection

We present a complete study of Delta S = 2 and Delta B = 2 processes in warped extra dimensional models with a custodial protection of Z b_L anti-b_L, including epsilon_K, Delta M_K, Delta M_s, Delta M_d, A_SL^q, Delta Gamma_q, A_CP(B_d -> psi K_S) and A_CP(B_s -> psi phi). These processes are affected by tree level contributions from Kaluza-Klein gluons and new heavy electroweak gauge bosons Z_H and Z', with the latter implied by the custodial protection mechanism. We confirm recent findings that the fully anarchic approach where all the hierarchies in quark masses and weak mixing angles are geometrically explained seems implausible and we confirm that the KK mass scale M_KK generically has to be at least ~ 20TeV to satisfy the epsilon_K constraint. We point out, however, that there exist regions in parameter space with only modest fine-tuning in the 5D Yukawa couplings which satisfy all existing Delta F = 2 and electroweak precision constraints for scales M_KK ~ 3TeV in reach of the LHC. Simultaneously we find that A_CP(B_s -> psi phi) and A^s_SL can be much larger than in the SM as indicated by recent results from CDF and D0 data. We point out that for B_{d,s} physics observables the new heavy electroweak gauge bosons Z_H and Z' can compete with KK gluons, while the Z contributions are negligible in both K and B_{d,s} systems due to the custodial protection. As a by-product we show the relation of the RS flavour model to the Froggatt-Nielsen mechanism and we provide analytic formulae for the effective flavour mixing matrices in terms of the fundamental 5D parameters